In Derek Mahon's poem "A Disused Shed in Co. Wexford" a film crew working on an estate that had once belonged to an "expropriated mycologist" comes across a shed that has not been opened since civil war days. When they open its door, they find it full of mushrooms that have for years been growing toward the single point of light provided by the shed's keyhole. "Lost people of Treblinka and Pompeii" Mahon addresses them, as they, in turn, plead with him: "Let not our naive labours have been in vain".

However one alters or even demolishes the shed there is always the memory of that fumble of pale arms. It is the memory of similarly pale arms - the tattooed arms of human prisoners - that make Primo Levi's writing unforgettable. Their suffering underwrites the beauty of his prose. But people suffer much without ever being able to order and shape experience into language. Levi himself struggled in his early work as he shifted between post-war neo-realism and a kind of science-fiction fantasy, developing what he considered to be "light and entertaining sketches".

There was little lightness about the first efforts. The earliest story in A Tranquil Star is about a wartime partisan who kills himself and several German soldiers by detonating a grenade. For the partisan it is an improvised act rather than a strategy, and the story, in appropriately realist style, depicts the act as a moment of noble sacrifice. Curiously instructive for us in an age of suicide bombers, it is an honest and dignified piece of storytelling without any outstanding promise.

Levi is fascinated by courage as a form of initiation. "Bear Meat", the next story in the collection, was first published 12 years later and is about the risks of mountaineering. Its manner of telling is changed - Levi did experiment continually with narrative technique - in that it floats its stories at the reader while still giving an account with carefully registered detail. The realism begins to shift a gear. But the rest of the early stories in the book are much more allegorical-fantastical and seem rather leaden, the ideas too abstract, the execution too plodding. It is as if Levi were trying on a range of voices, none of which quite fitted him. There is a satire on censorship, another on a strange weapon, and a fantasy of bringing together his favourite reading in a single park. All might have been shorter and lighter.

And then the change. In 1975 Levi retired from his directorship of the paint factory that he had entered as an industrial chemist 30 years earlier and became a full-time writer. Suddenly, we meet the mature writer of The Periodic Table, inventive and playful, indeed a little mischievous, but fully alive, at once humane and misanthropic, the writing spare, with something bitter lurking in its veins.

It is clear what that is. The shortest story, "Fra Diavolo on the Po", recalls being called up into the navy in 1936, undergoing pointless military exercises, then, after "captivity in Germany", being asked to register for the draft again, a summons he can refuse only by showing the concentration camp tattoo on his arm. The tattoo and the captivity underline Levi's gloominess about the human condition. This is seen most bleakly in "One Night", the story of the stripping and demolishing of a train by an unnamed crowd who, having dismantled the engine, "flung themselves against one another with deliberate blows", some "blindly striking themselves". The story suggests that is how humanity behaves. The fact is, it behaves badly. In "The Sorcerers" a pair of ethnographers come within inches of death when left isolated with a Bolivian tribe. Humans should strain to advance, we feel. The tribe represents the conditions the voice of the story wants to escape. But civilised society is no better. There are efficient bureaucracies that determine fates in "The Bureau of Vital Statistics", sadistic gladiatorial games in the future, planets waiting to collide and melt. The human is what gets lost: the glimpsed poem in "The Fugitive", the old Lithuanian woman in "The Girl in the Book", and the oddly human kangaroo at the "Buffet Dinner". Collectives are generally bad. It is the lost, stray individual that is good but doomed.

The writing in the later stories - to the credit of the translators - has the translucence we associate with Levi at his best. But the keynote is the one heard in the penultimate story. In "The Molecule's Defiance" the chemist thinks of atoms, where it is "as if every molecule were standing there with its hands outstretched, ready to grasp the hand of the molecule passing by to form a chain". It is those pale limbs again, Mahon's mushrooms, the terrible reaching for light in a world where man is wolf unto man.

· George Szirtes's book of poems Reel won the TS Eliot Prize in 2004. His translation of Sándor Márai's The Rebels has just been published by Knopf